Procedural modeling allows computer-generated objects having complex phenomena and geometry to be created using a set of parametric, conditional or stochastic rules. As such, procedural approaches in geometry modeling create an abstraction layer between the user and the geometry that alleviates the need for tedious direct geometric editing. A wide variety of object categories can be modeled using procedural modeling including organic shapes, such as trees and animated characters, as well as man-made shapes, such as buildings, furniture, and jewelry. Once a procedural model for an object category is available, it can be used to create a rich set of unique objects by varying the parameters of the procedural rule set. For instance, a user interface may be provided that exposes and allows a user to control the various parameters of a procedural model in order to generate objects. However, often times the underlying parametric space is very high-dimensional and its mapping to geometry is complex, thus making the resulting geometry difficult to control and explore using direct parameter editing. In other words, given a high number of procedural model parameters and the interaction between the parameters in forming objects, it may be difficult and/or very time-consuming for a user to generate an object of a desired shape.